100+ Time and Work Questions for Competitive Exams - 1

Ans: D

(A + B + C)’s 1 day’s work = $${1}/{6}$$

(A + B)’s 1 day’s work = $${1}/{8}$$

(B + C)’s 1 day’s work = $${1}/{12}$$

∴ (A + C)’s 1 day’s work

= $$(2 × {1}/{6})$$ - $$({1/8} + {1/12})$$

= $$({1/3} – {5/24})$$ = $${3}/{24}$$ = $${1}/{8}$$

So, A and C together will do the work in 8 days.

Ans: D

A’s 1 day’s work = $${1}/{5}$$; B’s 1 day’s work = $${1}/{20}$$

(A + B)’s 1 day’s work = $$({1/15} + {1/20})$$ = $${7}/{60}$$

(A + B)’s 4 day’s work = $$({7}/{60} × 4)$$ = $${7}/{15}$$

∴ Remaining work = $$(1 – {7}/{15})$$ = $${8}/{15}$$

Ans: B

1 man’s 1 day’s work = $${1}/{100}$$

(10 men + 15 women)’s 1 day’s work = $${1}/{6}$$

15 women’s 1 day’s work = $$({1}/{6} – {10}/{100})$$ = $$({1}/{6} – {1}/{10})$$ = $${1}/{15}$$

1 woman’s 1 day’s work = $${1}/{225}$$

∴ 1 woman alone can complete the work in 225 days.

Ans: B

Number of rosogollas eaten by Rosa in 1 minute = $${32}/{60}$$

Number of rosogollas eaten by Lila in 1 minute = $${32}/{180}$$

Number of rosogollas eaten by Rosa and Lila together in 1 minute = $$({32/60} + {32/180})$$ = $${128}/{180}$$

Required time = $$(32 – {128}/{180})$$ = $$({32 × 180}/ {128})$$min = 45 min.

Ans: C

(A + B)’s 20 day’s work = $$({1}/ {30} × 20)$$ = $${2} / {3}$$

Remaining work = $$(1 – {2} / {3})$$ = $${1} / {3}$$

Now, $${1} / {3}$$ work is done by A in 20 days.

Whole work will be done by A in (20 × 3) = 60 days.